In a circle with center O AC and BD are diameters. The center angle of the AOD is 142 degrees. Find the inscribed corner ACB.
| January 17, 2021 | education
∠АОВ and ∠АОD are adjacent, which means ∠АОВ + ∠АОD = 180 °.
Therefore, ∠АВ = 180 ° – ∠АОD = 180 ° – 142 ° = 38 °.
∠АСВ rests on the arc AB and the central ∠АОВ rests on the arc AB.
Because ∠АСВ – inscribed, and the inscribed angle is equal to half of the central angle resting on the same arc, then we find its value:
∠АСВ = ½ * ∠АВ = ½ * 38 ° = 19 °.
Answer: ∠АСВ = 19 °.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
